Mirjam Moerbeek

The Consequence of Ignoring a Level of Nesting in Multilevel Analysis

Multilevel analysis is an appropriate tool for the analysis of hierarchically structured data. There may, however, be reasons to ignore one of the levels of nesting in the data analysis. In this article a three level model with one predictor variable is used as a reference model and the top or intermediate level is ignored in the data analysis. Analytical results show that this has an effect on the estimated variance components and that standard errors of regression coefficients estimators may be overestimated, leading to a lower power of the test of the effect of the predictor variable. The magnitude of these results depends on the ignored level and the level at which the predictor variable varies, and on the values of the variance components and the sample sizes.

A comparison between traditional methods and multilevel regression for the analysis of multicenter intervention studies

This article reviews three traditional methods for the analysis of multicenter trials with persons nested within clusters, i.e., centers, namely naïve regression (persons as units of analysis), fixed effects regression, and the use of summary measures (clusters as units of analysis), and compares these methods with multilevel regression. The comparison is made for continuous (quantitative) outcomes, and is based on the estimator of the treatment effect and its standard error, because these usually are of main interest in intervention studies. When the results of the experiment have to be valid for some larger population of centers, the centers in the intervention study have to present a random sample from this population and multilevel regression may be used. It is shown that the treatment effect and especially its standard error, are generally incorrectly estimated by the traditional methods, which should, therefore, not in general be used as an alternative to multilevel regression.

Stepped wedge designs could reduce the required sample size in cluster randomized trials

OBJECTIVE The stepped wedge design is increasingly being used in cluster randomized trials (CRTs). However, there is not much information available about the design and analysis strategies for these kinds of trials. Approaches to sample size and power calculations have been provided, but a simple sample size formula is lacking. Therefore, our aim is to provide a sample size formula for cluster randomized stepped wedge designs. STUDY DESIGN AND SETTING We derived a design effect (sample size correction factor) that can be used to estimate the required sample size for stepped wedge designs. Furthermore, we compared the required sample size for the stepped wedge design with a parallel group and analysis of covariance (ANCOVA) design. RESULTS Our formula corrects for clustering as well as for the design. Apart from the cluster size and intracluster correlation, the design effect depends on choices of the number of steps, the number of baseline measurements, and the number of measurements between steps. The stepped wedge design requires a substantial smaller sample size than a parallel group and ANCOVA design. CONCLUSION For CRTs, the stepped wedge design is far more efficient than the parallel group and ANCOVA design in terms of sample size.

Design Issues for Experiments in Multilevel Populations

For the design of experiments in multilevel populations the following questions may arise: What is the optimal level of randomization? Given a certain budget for sampling and measuring, what is the optimal allocation of units? What is the required budget for obtaining a certain power on the test of no treatment effect? In this article these questions will be dealt with for populations with two or three levels of nesting and continuous outcomes. Multilevel models are used to model the relationship between experimental condition and the outcome variable. The estimator of the regression, coefficient associated with treatment condition, a parameter assumed to be fixed in this paper; is of main interest and should be estimated as efficiently as possible. Therefore, its variance is used as a criterion for optimizing the level of randomization and the allocation of units.

Effects of anger and anger regulation styles on pain in daily life of women with fibromyalgia: a diary study.

Background: Fibromyalgia is characterized by an amplified pain response to various physical stimuli. Through biological and behavioural mechanisms, patients with fibromyalgia may also show an increase of pain in response to emotions. Anger, and how it is regulated, may be particularly important in chronic pain.

Influence of Motivational Interviewing on Explicit and Implicit Alcohol-Related Cognition and Alcohol Use in At-Risk Adolescents

Both implicit and explicit cognitions play an important role in the development of addictive behavior. This study investigated the influence of a single-session motivational interview (MI) on implicit and explicit alcohol-related cognition and whether this intervention was successful in consequently decreasing alcohol use in at-risk adolescents. Implicit and explicit alcohol-related cognitions were assessed at pretest and one month posttest in 125 Dutch at-risk adolescents ranging in age from 15 to 23 (51 males) with adapted versions of the Implicit Association Test (IAT) and an expectancy questionnaire. Motivation to change, alcohol use and alcohol-related problems were measured with self-report questionnaires, at pretest, at posttest after one month, and at the six-month follow-up. Although the quality of the intervention was rated positively, the results did not yield support for any differential effects of the intervention on drinking behavior or readiness to change at posttest and six-month follow-up. There were indications of changes in implicit and explicit alcohol-related cognitions between pretest and posttest. Our findings raise questions regarding the use of MI in this particular at-risk adolescent population and the mechanisms through which MI is effective. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

Optimal experimental designs for multilevel models with covariates

In this paper optimal experimental designs for multilevel models with covariates and two levels of nesting are considered. Multilevel models are used to describe the relationship between an outcome variable and a treatment condition and covariate. It is assumed that the outcome variable is measured on a continuous scale. As optimality criteria D-optimality, and L-optimality are chosen. It is shown that pre-stratification on the covariate leads to a more efficient design and that the person level is the optimal level of randomization. Furthermore, optimal sample sizes are given and it is shown that these do not depend on the optimality criterion when randomization is done at the group level.

Optimal Experimental Designs for Multilevel Logistic Models

When designing experiments in multilevel populations the following questions arise: what is the optimal level of randomization, and what is the optimal allocation of units? In this paper these questions will be dealt with for populations with two levels of nesting and binary outcomes. The multilevel logistic model, which is used to describe the relationship between treatment condition and outcome, is linearized. The variance of the regression coefficient associated with treatment condition in the linearized model is used to find the optimal level of randomization and the optimal allocation of units. An analytical expression for this variance can only be obtained for the first-order marginal quasi-likelihood linearization method, which is known to be biased. A simulation study shows that penalized quasi-likelihood linearization and numerical integration of the likelihood lead to conclusions about the optimal design that are similar to those from the analytical derivations for first-order marginal quasi-likelihood.

The Design of Cluster Randomized Crossover Trials

The inefficiency induced by between-cluster variation in cluster randomized (CR) trials can be reduced by implementing a crossover (CO) design. In a simple CO trial, each subject receives each treatment in random order. A powerful characteristic of this design is that each subject serves as its own control. In a CR CO trial, clusters of subjects are randomly allocated to a sequence of interventions. Under this design, each subject is either included in only one of the treatment periods (CO at cluster level) or in both periods (CO at subject level). In this study, the efficiency of both CR CO trials relative to the CR trial without CO is demonstrated. Furthermore, the optimal allocation of clusters and subjects given a fixed budget or desired power level is discussed.

Powerful and cost-efficient designs for longitudinal intervention studies with two treatment groups.

Three issues need to be decided in the design stage of a longitudinal intervention study: the number of persons, the number of repeated measurements per person, and the duration of the study. The degree to which polynomial effects vary across persons and the drop-out pattern also influence the statistical power to detect intervention effects. This article presents a framework that allows researchers to calculate the power of a proposed design and compare alternative designs on the basis of their costs and sample sizes. A multilevel regression model with polynomial effects varying across persons is used to relate response to time. The persons’ length of stay in the study is modeled using a survival function.